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The theoretical derivation of the start‐up laminar flow of incompressible viscous fluid in a long pipe as suggested by Szymanski, could not be verified experimentally. This leads to the checking of assumption of constant pressure gradient across the ends of the pipe, on the basis of which the theoretical development was made. Recently, the problem was again investigated for viscous fluid by Otis. In the present paper, the laminar start‐up flow of elastico‐viscous fluid in a pipe, without assuming constant pressure gradient across its ends, has been investigated. The non‐linear governing equations are solved numerically and the effects of start‐up flow parameters and elastico‐viscous parameter on the velocity distribution have been studied.

The research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The paper describes the methodology, and gives illustrative results for simple geometries.

The pseudospectral matrix element method of discretisation is selected as the basis for the CFD technique adopted, because of its high spectral accuracy. It is implemented as a means of solving the Navier‐Stokes equations coupled with the modified compressibility method.

The viscous solver has been validated for the benchmark cases of uniform flow past a cylinder at a Reynolds number of 40, and 2D cavity flows. Results for sloshing of a viscous fluid in a tank have been successfully compared with those from a linearised analytical solution. Application of the method is illustrated by the results for the interaction of an impulsive wave with a surface piercing circular cylinder in a cylindrical tank.

The paper demonstrates the viability of the approach adopted. The limitation of small amplitude waves should be tackled in future work.

The results will have particular significance in the context of validating computations from more complex schemes applicable to arbitrary geometries.

The new methodology and results are of interest to the community of those developing numerical models of flow past marine structures.

This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.

Exact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).

Two total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.

No thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

An aerothermodynamic design code for axisymmetric projectiles has been developed using a viscous‐inviscid interaction scheme. Separate solution procedures for the inviscid and the viscous (boundary layer) fluid dynamic equations are coupled by an iterative solution procedure. Non‐equilibrium, equilibrium and perfect gas boundary layer equations are included. The non‐equilibrium gas boundary layer equations assume a binary mixture (two species; atoms and molecules) of chemically reacting perfect gases. Conservation equations for each species include finite reaction rates applicable to high temperature air. The equilibrium gas boundary layer equations assume infinite rate reactions, while the perfect gas equations assume no chemical reactions. Projectile near‐wall and surface flow profiles (velocity, pressure, density, temperature and heat transfer) representing converged solutions to both the inviscid and viscous equations can be obtained in less than two minutes on minicomputers. A technique for computing local reverse flow regions is included. Computations for yawed projectiles are accomplished using a coordinate system transformation technique that is valid for small angle‐of‐attack. Computed surface pressure, heat transfer rates and aerodynamic forces and moments for 1.25 &le Mach No. &le 10.5 are compared to wind tunnel and free flight measurements on flat plate, blunt‐cone, and projectile geometries such as a cone‐cylinder‐flare.

We introduce a second‐order accurate time‐marching pressure‐correction algorithm to accommodate weakly‐compressible highly‐viscous liquid flows at low Mach number. As the incompressible limit is approached (Ma ≈ 0), the consistency of the compressible scheme is highlighted in recovering equivalent incompressible solutions. In the viscous‐dominated regime of low Reynolds number (zone of interest), the algorithm treats the viscous part of the equations in a semi‐implicit form. Two discrete representations are proposed to interpolate density: a piecewise‐constant form with gradient recovery and a linear interpolation form, akin to that on pressure. Numerical performance is considered on a number of classical benchmark problems for highly viscous liquid flows to highlight consistency, accuracy and stability properties. Validation bears out the high quality of performance of both compressible flow implementations, at low to vanishing Mach number. Neither linear nor constant density interpolations schemes degrade the second‐order accuracy of the original incompressible fractional‐staged pressure‐correction scheme. The piecewise‐constant interpolation scheme is advocated as a viable method of choice, with its advantages of order retention, yet efficiency in implementation.

The purpose of this paper is to explore the characteristics of hypersonic flow past a blunt body.

The implicit finite volume schemes are derived from axisymmetric Navier–Stokes equations by means of AUSM+ and LU-SGS methods, and programmed in FORTRAN. Based on the verified result that a 2D axisymmetric chemical equilibrium flow has a good agreement with the literature, the characteristics of hypersonic flow past a sphere are simulated by using four different models which involve four factors, namely, viscous, inviscid, equilibrium and calorically perfect gas.

Compared with the calorically perfect gas under hypervelocity condition, the shock wave of the equilibrium gas is more close to the blunt body, gas density and pressure become bigger, but gas temperature is lower due to the effect of real gas. Viscous effects are not obvious in the calculations of the equilibrium gas or the calorically perfect gas. In a word, the model of equilibrium gas is more suitable for hypersonic flow and the calculation of viscous flow has a smaller error.

The computer codes are developed to simulate the characteristics of hypersonic flows, and this study will be helpful for the design of the thermal protection system in hypersonic vehicles.

The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters.

The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders.

As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases.

The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

The aim of this article is to present the results of a parametric analysis of the entropy generation due to mixed convection in the entry‐developing region between two differentially heated isothermal vertical plates.

The entropy generation was estimated via a numerical solution of the mass, momentum and energy conservation equations governing the flow and heat transfer in the vertical channel between the two parallel plates. The resultant temperature and velocity profiles were used to estimate the entropy generation and other heat transfer parameters over a wide range of the operating parameters. The investigated parameters include the buoyancy parameter (Gr/Re), Eckert number (Ec), Reynolds number (Re), Prandtl number (Pr) and the ratio of the dimensionless temperature of the two plates (θ_T).

The optimum values of the buoyancy parameter (Gr/Re) optimum at which the entropy generation assumes its minimum for the problem under consideration have been obtained numerically and presented over a wide range of the other operating parameters. The effect of the other operating parameters on the entropy generation is presented and discussed as well.

The results of this investigation are limited to the geometry of vertical channel parallel plates under isothermal boundary conditions. However, the concept of minimization of entropy generation via controlling the buoyancy parameter is applicable for any other geometry under any other thermal boundary conditions.

The results presented in this paper can be used for optimum designs of heat transfer equipment based on the principle of entropy generation minimization with particular focus on the optimum design of plate and frame heat exchanger and the optimization of electronic packages and stacked packaging of laminar‐convection‐cooled printed circuits.

This paper introduces the entropy generation minimization via controlling the operating parameters and clearly identifies the optimum buoyancy parameter (Gr/Re) at which entropy generation assumes its minimum under different operating conditions.

The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.

The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial penetration through a boundary, hence the implementation of porous wall boundaries. The finite element method is used for investigating and interpreting penalty approaches to boundary conditions.

The generalised penalty approach is verified by means of a novel variant of the circular‐Couette flow problem, having partial slip on one of the cylindrical boundaries, for which an analytic solution is derived. Further verificationis provided by consideration of viscous flow over a sphere with partial slip on the surface, and comparison of numerical and classical solutions. Numerical studies illustrate the versatility of the approach.

The penalty approach is applied to some different boundaries: partial slip and partial penetration with no/full slip/penetration as limiting cases; free surface; space‐ and time‐varying boundary conditions which allow progressive contact over time. Application is made to curved and inclined boundaries. Sensitivity of flow to penalty parameters is an avenue for continued research, as is application of the penalty approach for non‐Newtonian flows.

This is the first work to show the relation between penalty formulation of boundary conditions and physical boundary conditions. It provides a method that overcomes past difficulties in implementing partial slip on boundaries of general shape, and which handles progressive contact. It also provides useful benchmark problems for future studies.

The purpose of this paper is to investigate the effect of the viscous dissipation of laminar flow through a straight regular polygonal duct on forced convection with constant axial wall heat flux with constant peripheral wall temperature using the boundary element method (BEM).

Both the wall heating case and the wall cooling case are considered. Applying the velocity profile obtained for the duct laminar flow and the energy equation with the viscous dissipation term is solved exactly for the constant wall heat flux using the BEM. The numerical values are obtained by means of a computer program, written by the authors in Fortran. The results of the BEM approach are verified by analytic models. Nusselt numbers are obtained for flows with a different number of sides of a regular polygonal duct and Brinkman numbers.

When the difference in temperature between the wall temperature and the fluid bulk temperature changes the sign, then the functions of the Nusselt number with the Brinkman number generated some singularities (Br_qLs). For the Brinkman number referring to the total wall linear power, with the increasing value of the number of sides of a regular polygonal duct, Br_qLs decreases in the range of 3 ≤ n < ∞. If the Br_qL < Br_qLs, it is possible to note that, in general, the Nusselt number is higher for cross-sections having a lower value of the number of sides of a regular polygonal duct. For Br_qL > Br_qLs, this rule is reversed.

This paper illustrates the effects of viscous dissipation on laminar forced convective flow in regular polygon ducts with a different number n of sides. A compact relationship for the Nusselt number vs the Brinkman number referring to the temperature difference between the wall temperature and the fluid bulk temperature and the Brinkman number, which is based on the total wall linear power, have been proposed.